Abstract:A new method for resolving nonproportionally damping matrix into proportional damping matrix and remainder dampng matrix and a new method for solving nonproportionally damped systems were proposed respectively.After introducing the perturbation method in to the nonproportional damping matrix and response vector, the nonproportionally damped system was reduced to a series of proportionally damped systems,which can be decoupled by using modal transformation. Based on this,an approximatelly analytical solution was obtined. The examples show that the solution obtained by this method agrees very well with that by the numerical method.